An $L^∞$ Bound for the Cahn-Hilliard Equation with Relaxed Non-Smooth Free Energy

An $L^∞$ Bound for the Cahn-Hilliard Equation with Relaxed Non-Smooth Free Energy

Year:    2017

International Journal of Numerical Analysis and Modeling, Vol. 14 (2017), Iss. 2 : pp. 243–254

Abstract

Phase field models are widely used to describe multiphase systems. Here a smooth indicator function, called phase field, is used to describe the spatial distribution of the phases under investigation. Material properties like density or viscosity are introduced as given functions of the phase field. These parameters typically have physical bounds to fulfil, e.g. positivity of the density. To guarantee these properties, uniform bounds on the phase field are of interest. In this work we derive a uniform bound on the solution of the Cahn-Hilliard system, where we use the double-obstacle free energy, that is relaxed by Moreau-Yosida relaxation.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2017-IJNAM-419

International Journal of Numerical Analysis and Modeling, Vol. 14 (2017), Iss. 2 : pp. 243–254

Published online:    2017-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

Keywords:    Cahn-Hilliard Moreau-Yosida relaxation phase field equations uniform bounds.